This study is devoted to the issue of constructing robust T-optimal discriminating designs for two competing trigonometric regression models, which differ by three trigonometric functions at most. To solve this problem, we propose using a Bayesian and standardized maximin approaches. The robust T-optimal discriminating designs were found explicitly in a number of particular cases. In the general case, on account of the complexity of the optimization problem, the corresponding optimal designs are not easy to find and have to be determined numerically. The results are illustrated by means of several examples.